Expected Return Calculator
This expected return calculator turns a series of annual returns into the arithmetic mean and the compounded geometric return, side by side.
What it does
The Expected Return Calculator turns a series of annual returns into a single expected figure. It reports both the arithmetic mean, the simple average investors usually quote, and the geometric mean, the rate that actually compounds a portfolio over time.
Data sources & parameters
This calculator uses standard financial formulas and runs entirely in your browser. It needs no external rate data — your result is computed only from the values you enter above.
We always strive to use the latest data for every variable so our results and reports are as accurate as possible. Even so, errors are possible — you should not rely on this tool or its report alone, and we accept no liability for any decision made based on it.
The formula
arithmetic_mean = Σr ÷ n ; geometric_return = (∏(1 + r/100))^(1/n) − 1, expressed as a percentage
How it works
It sums the yearly returns and divides by the number of years to get the arithmetic mean. It then multiplies the growth factors of each year, takes the nth root, and converts back to a percentage to get the geometric return that reflects true compounding.
Where it is used
- Estimating the forward-looking return of a fund from its track record
- Seeing how volatility drags the compounded return below the simple average
- Comparing two portfolios on a fair, compounding-adjusted basis
Worked example
A portfolio returns 10%, 12%, 8%, 15% and 5% over five years. The arithmetic mean is …, while the geometric return that actually compounds the money is … — slightly lower because return swings always cost you.
What the expected return calculator does
The expected return calculator condenses several years of investment performance into one forward-looking figure. You enter the annual return for each of five years, and the tool reports two averages. The arithmetic mean tells you what a typical year looked like. The geometric mean is the constant rate that would have grown your money the same way the actual, uneven sequence of returns did.
Most people quote the arithmetic average. If a fund earned 10%, 12%, 8%, 15% and 5%, they add those up, divide by five, and say the fund "returns 10% a year." That is true in a narrow sense, but the rate at which their money grew is the geometric return, and it is almost always a little lower.
How the calculation works
The arithmetic mean is the simple average: add the five returns and divide by five. In the example, 10 + 12 + 8 + 15 + 5 equals 50, and dividing by five gives 10%.
The geometric mean multiplies growth factors instead of adding percentages. A 10% return becomes a growth factor of 1.10, a 12% return becomes 1.12, and so on. The tool multiplies all five factors to find the total growth over the period, takes the fifth root to find the single annual rate that produces the same total, and converts it back into a percentage. For the same example the geometric return is about 9.95%, slightly below the arithmetic 10%.
In formula terms, the arithmetic mean is the sum of the returns divided by the number of years. The geometric return is the nth root of the product of (1 + r) for every year, minus one, expressed as a percentage.
Why the geometric return is lower
Whenever returns vary from year to year, the geometric mean falls below the arithmetic mean, and the more they vary, the wider the gap. Percentage gains and losses are not symmetric: an investment that falls 50% in one year needs to rise 100% the next to break even. A volatile path therefore compounds to less than a smooth one with the same simple average.
Suppose one portfolio returns a steady 5% every year, and another returns 30% one year and loses 20% the next. Both have an arithmetic average of 5%. The volatile portfolio grows by a factor of 1.30 and then shrinks by 0.80, a factor of 1.04 over two years, or roughly 2% a year compounded. The steady portfolio compounds at the full 5%. The geometric return shows that difference; the arithmetic mean hides it.
When to use each number
To estimate how a lump sum will grow across many years, use the geometric return, because that is the rate that compounds. Projecting retirement savings, comparing funds over a decade, or working out how long it takes to double your money all call for the geometric figure.
The arithmetic mean is the better estimate for the expected return of a single future period on its own, and it is the input classical portfolio theory uses when combining assets. A careful planner keeps both in view: the arithmetic mean as an unbiased estimate of next year, and the geometric mean as the realistic long-run growth rate.
Reading your results
The expected return shown is the arithmetic mean. The geometric return is the compounded rate after the effect of volatility. The arithmetic mean is repeated alongside so you can compare the two, and the bar chart plots each year's return so you can see which years pulled the average up or down.
A narrow gap between the two means the returns were fairly stable. A wide gap means the investment was volatile and the simple average overstates what you would have earned. Sales material almost always quotes the higher arithmetic figure.
Limitations
The tool works only with the numbers you enter. It does not account for fees, taxes, inflation, or the order in which returns arrive relative to your contributions. If you are drawing money out of a portfolio, the sequence of returns matters enormously, and neither average fully captures that risk. For a net real return, subtract costs, taxes, and inflation from each yearly figure before entering it.
A five-year average describes what happened; it does not forecast what will happen. Treat the expected return as one input among many and check it against long-run market history.
About This Expected Return Calculator
Use this expected return calculator to get an instant estimate based on the figures you enter. Adjust the inputs above to match your situation, or browse all our calculators to plan your next step.
Frequently asked questions
What is expected return?
What is the difference between arithmetic and geometric return?
Why is the geometric return lower than the average?
Which return should I use for planning?
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How many years should I enter?
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